摘要：
本文考虑二阶常微分方程三点边值问题{u″(t)+h(t)f(u)=0,t∈(0,1),u′(0)=0,u(1)=λu(η),其中η∈[0,1),参数λ∈[0,1),函数f∈C([0,∞),[0,∞))满足f(s)>0,s>0,h∈C([0,1],[0,∞))在[0,1]的任意子区间内不恒为零.在满足条件f0=0,f∞=∞ 时,本文讨论了该边值问题解所构成的连通分支随着参数λ在[0,1]内的变化而变化的情形,建立了正解的全局结构.主要结果的证明基于锥上的不动点指数定理以及解集连通性质.%In this paper ,we consider the second-order three-point boundary value problem {u″(t) + h(t) f (u) = 0 ,t ∈ (0 ,1) , u′(0) = 0 ,u(1) = λu(η) , w hereη∈ [0 ,1) ,λ∈ [0 ,1) is a parameter ,f ∈ C([0 ,∞) ,[0 ,∞)) satisfies f (s) > 0 for s > 0 ,and h ∈C([0 ,1] ,[0 ,∞)) is not identically zero on any subinterval of [0 ,1] .We give information on the problem as to w hat happens to the norms of positive solutions asλvaries in [0 ,1] under the conditions of f0 = 0 , f ∞ = ∞ .T he proof of the main results is based upon the fixed point index theory on cone and connectiv-ity properties of the solution set .
